Mathematics Commons^™

Sports Analytics With Computer Vision, Colby T. Jeffries

Senior Independent Study Theses

Computer vision in sports analytics is a relatively new development. With multi-million dollar systems like STATS’s SportVu, professional basketball teams are able to collect extremely fine-detailed data better than ever before. This concept can be scaled down to provide similar statistics collection to college and high school basketball teams. Here we investigate the creation of such a system using open-source technologies and less expensive hardware. In addition, using a similar technology, we examine basketball free throws to see whether a shooter’s form has a specific relationship to a shot’s outcome. A system that learns this relationship could be used to …

Covers For Unit Arcs, Sutara Patlertsin

Chulalongkorn University Theses and Dissertations (Chula ETD)

In 1966, Leo Moser posed a famous problem asking “ What is the region of smallest area which will accommodate every planar arc of length one? ". In 2003, Norwood and Poole showed that the cover whose upper boundary is the circular arc and the lower boundary is composed of 2 symmetric parabolic arcs between 2 symmetric circular arcs is the smallest cover known which are not convex. In this work, we study the region obtained by modifying the cover of Norwood and Poole and its area is 0.2596605. We investigate the Λ-property and relating properties which are very useful …

Local And Global Dynamic Bifurcations Of Nonlinear Evolution Equations, Desheng Li, Zhi-Qiang Wang

Mathematics and Statistics Faculty Publications

We present new local and global dynamic bifurcation results for nonlinear evolution equations of the form ut + Au = fλ(u) on a Banach space X, where A is a sectorial operator, and λ ∈ R is the bifurcation parameter. Suppose the equation has a trivial solution branch {(0, λ) : λ ∈ R}. Denote Φλ the local semiflow generated by the initial value problem of the equation. It is shown that if the crossing number n at a bifurcation value λ = λ0 is nonzero and moreover, S0 = {0} is an isolated invariant set of Φλ0 , then …

Did They Learn Anything? - Learning Assessment In A General Business Analytics Course, Zsolt Ugray, Brynja Kohler

Mathematics and Statistics Faculty Publications

There is a projected need for 2 to 4 million of business translators who are not only experts in their business disciplines but also conversant and familiar with the use and limitations of business analytics. Preparing business students to step into the business translator role requires a general introductory analytics course. This paper presents a multi-component learning assessment to evaluate the depth of learning from such a course. This learning assessment is novel in a sense that it uses four distinct tools, both quantitative and qualitative ones, to measure students’ improvements in a comprehensive manner.

Thin Cloud Removal Using Local Minimization And Image Transformation In Hsi Color Space, Thanet Markchom

Chulalongkorn University Theses and Dissertations (Chula ETD)

In the use of satellite images, clouds can be an obstacle due to their opacity property that can block the visibility of ground objects in case of thick clouds and can also be blended with the underlying details in case of thin clouds. In this research, we propose a novel method to remove thin clouds and retrieve the actual information by taking the advantage of HSI color space instead of RGB color space. The proposed method aims to estimate the cloud appearance called the scattering light, remove thin clouds from intensity channel to avoid an effect to the original color, …

Cyclic Clique Decompositions Of Powerof Cycles, Apiwat Peereeyaphat

Chulalongkorn University Theses and Dissertations (Chula ETD)

A clique decomposition P of a graph G is a collection of cliques of G such that each edge of G belongs to exactly one clique in the collection. We say that P is cyclic if there is an isomorphism : V (G)→ V (G) such that Kk{α (v₁), α (v₂), α (v₃), ... , α (vk)g is a clique in P whenever Kk{v₁; v₂; v₃; :::; vk} is. The k-power of an n-cycle, Ck n, is the graph having the same vertex set as Cn and uv is an edge in Ck n if and only if dCn(u; v) …

Defective Colorings On Complete Bipartite And Multipartite K-Uniform Hypergraphs, Artchariya Muaengwaeng

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this thesis, we modify the definition of a defective coloring and a defective chromatic number on graphs to a defective coloring and a defective chromatic number on hypergraphs. First, we find the defective chromatic number on a complete bipartite k-uniform hypergraph and the defective chromatic number on a complete bipartite k-uniform hypergraph of which each color class is acyclic. Second, we determine the defective chromatic number and the defective chromatic number of which each color class is acyclic on a complete k-partite k-uniform hypergraph whose each edge has k vertices from k different partite sets. Finally, we determine the …

Critical Exponent For Nonlinear Nonlocal Equations, Auttawich Manui

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this thesis, we study the nonlinear nonlocal equation ∂t u=J*u-u+u¹+p where p>0 and J is nonnegative, bounded, and radially symmetric with unit integral. The Fourier transform of J satisfies J ̂(ξ)=1-A|ξ|^β (ln1/|ξ| 〗 )^μ+o(〖|ξ|〗^β (ln〖1/(|ξ|)〗 )^μ ) as ξ→0, for 0<β≤2, μ∈R, and A>0. In this study, we establish the local existence, uniqueness, and the comparison principle of solutions. Furthermore, we show that the Fujita critical exponent for this equation is β/n when μ<0. For the case μ>1, we discover that the critical exponent is β/n , and the solutions belong to the global to the small initial data regime.

Streaming Data Classification Method Using Scalable Hyper-Ellipsoids With Linear Discriminant Projection Distance Ratio, Perasut Rungcharassang

Chulalongkorn University Theses and Dissertations (Chula ETD)

Learning streaming data with limited size of memory storage becomes an interesting problem. Although there have been several learning methods recently proposed, based on the interesting concept of discard-after-learn, the performance of these issues: the learning speed, number of redundant neurons, and classification accuracy of these methods can be further improved in terms of faster speed, less number of neurons, and higher accuracy. The following new four concepts and approaches were proposed in this dissertation: (1) a more generic structure of hyper-ellipsoidal function called Scalable Hyper-Ellipsoidal Function (SHEF) capable of handling the problem of curse of dimensionality by introducing a …

Generalized Symplectic Graphs And Generalized Orthogonal Graphs Over Finite Commutative Rings, Siripong Sirisuk

Chulalongkorn University Theses and Dissertations (Chula ETD)

Let R be a finite commutative ring with identity, n ∈ N and β a bilinear form on Rⁿ. In this dissertation, we count the numbers of free submodules and totally isotropic free submodules of Rⁿ of rank s by using the lifting idea. We define the generalized bilinear form graph whose vertex set is the set of totally isotropic free submodules of Rⁿ of rank s and the adjacency condition is given by some rank conditions. We study this graph when (Rⁿ, β) is a symplectic space and an orthogonal space. We can determine the degree of each vertex …

Variant Of D'Alembert Functional Equation On Compact Homogeneous Space, Sorawit Viwanthananut

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this work, we introduce a new functional equation on compact homogeneous spaces based on the d'Alembert functional equation on compact groups. We solve the functional equation by using tools from harmonic analysis.

กลยุทธ์การลงทุนส่วนบุคคลบนพื้นฐานเกณฑ์การจัดเก็บภาษีเงินได้, ปิยวดี สุขชาติ

Chulalongkorn University Theses and Dissertations (Chula ETD)

ตามที่กรมสรรพากรได้ระบุไว้ใน แบบแสดงรายการภาษีเงินได้บุคคลธรรมดา ปีภาษี 2559 สำหรับผู้มีเงินได้ตามมาตรา 40 (1) - (8) แห่งประมวลรัษฎากร (ภ.ง.ด.90) จะสามารถนำเงินไปลงทุนในแหล่งต่าง ๆ เพื่อลดเงินได้สุทธิก่อนที่จะนำไปคำนวณภาษี ในที่นี้ผู้ทำวิจัยสนใจการวางแผนการลงทุนเพื่อจะได้รับประโยชน์ทางภาษีและผลตอบแทนสูงสุดโดยการนำเงินไปลงทุนใน 3 แหล่ง ประกอบด้วย ประกันชีวิต (Life insurance) กองทุนรวมเพื่อการเลี้ยงชีพ (Retirement Mutual Fund : RMF) และกองทุนรวมหุ้นระยะยาว (Long Term Equity Fund : LTF) โดยการหากลยุทธ์การลงทุนเพื่อแนะนำแหล่งลงทุนและหาสัดส่วนจำนวนเงินที่เหมาะสมที่ใช้ในการลงทุนในแหล่งต่าง ๆ ที่สอดคล้องกับแผนการลงทุนที่มีอยู่ในตลาดและนำเสนอแผนการลงทุนที่เหมาะสมสำหรับแต่ละบุคคล โดยที่ผู้ลงทุนไม่เสียสภาพคล่องทางการเงิน อีกทั้งยังได้รับประโยชน์ทางภาษีและผลตอบแทน นั่นคือการเสียภาษีน้อยลงจากเดิมและได้ผลตอบแทนจากการลงทุนสูงสุด เริ่มจากการหาแหล่งลงทุนที่เหมาะสมสำหรับแต่ละบุคคลตามระดับความเสี่ยงที่รับได้ สร้างตัวแบบทางคณิตศาสตร์เพื่อทำนายราคากองทุนต่าง ๆ แล้วทำนายผลตอบแทนกองทุนต่าง ๆ ตามแหล่งลงทุนที่เหมาะสมนั้นเพื่อหาว่ากองทุนใดให้ผลตอบแทนที่เหมาะสมที่สุดที่เหมาะกับบางช่วงของรายได้ เพื่อคำนวณสัดส่วนจำนวนเงินที่เหมาะสมสำหรับแต่ละบุคคลที่จะต้องใช้ในการลงทุนในแหล่งต่าง ๆ และนำเสนอแผนการลงทุนที่ให้ผลตอบแทนสูงสุดสามอันดับของแต่ละแหล่งลงทุน เพื่อให้ผู้ลงทุนใช้ประกอบการตัดสินใจ เมื่อผู้มีเงินได้นำเงินได้สุทธิไปลงทุนแล้วนั้น จะเป็นการลดเงินได้สุทธิให้น้อยลงหรือปรับลดขั้นเงินได้สุทธิ ทำให้อัตราภาษีที่จะต้องเสียในปีนั้น ๆ ลดลงและได้ผลตอบแทนสูงสุด

Column Generation With Heuristic For Two-Dimensional Guillotine Cutting Stock Problem With Usable Leftover, Supphakorn Sumetthapiwat

Chulalongkorn University Theses and Dissertations (Chula ETD)

The two-dimensional cutting stock problem with usable leftover (2DCSPUL) aims to minimize the waste from cutting in two aspects. The first aspect focuses on the suitable cutting patterns that provide the minimum waste while satisfying a requirement. The second aspect is to utilize the waste in the cutting process by turning the waste with sufficient size into a raw material or an item for the next cutting period. In this dissertation, the common two-stage guillotine cutting pattern which is found in many large industries is considered in this problem. Two definitions of fixed size usable leftover are introduced. A column …

Introductory Statistics, Barbara Illowsky, Susan Dean

Open Access Textbooks

Introductory Statistics follows scope and sequence requirements of a one-semester introduction to statistics course and is geared toward students majoring in fields other than math or engineering. The text assumes some knowledge of intermediate algebra and focuses on statistics application over theory. Introductory Statistics includes innovative practical applications that make the text relevant and accessible, as well as collaborative exercises, technology integration problems, and statistics labs.

Mat 2675 Calculus Iii, Spring 2019, Oer Syllabus, Caner Koca

Open Educational Resources

No abstract provided.

A Quest For Positive Definite Matrices Over Finite Fields, Erin Patricia Hanna

Theses and Dissertations

Positive definite matrices make up an interesting and extremely useful subset of Hermitian matrices. They are particularly useful in exploring convex functions and finding minima for functions in multiple variables. These matrices admit a plethora of equivalent statements and properties, one of which is an existence of a unique Cholesky decomposition. Positive definite matrices are not usually considered over finite fields as some of the definitions and equivalences are quickly seen to no longer hold. Motivated by a result from the theory of pressing sequences, which almost mirrors an equivalent statement for positive definite Hermitian matrices, we consider whether any …

States And The Numerical Range In The Regular Algebra, James Patrick Sweeney

Theses and Dissertations

In this dissertation we investigate the algebra numerical range defined by the Banach algebra of regular operators on a Dedekind complete complex Banach lattice, i.e., V (Lr(E), T) = {Φ(T) : Φ ∈ Lr(E)∗, ||Φ|| = 1 = Φ(I)}. For T in the center Z(E) of E we prove that V (Lr(E), T) = co(σ(T)). For T ⊥ I we prove that V (Lr(E), T) is a disk centered at the origin. We then consider the part of V (Lr(E), T) obtained by restricting ourselves to positive states Φ ∈ Lr(E)∗. In this case we show that we get a …

Graph Homomorphisms And Vector Colorings, Michael Robert Levet

Theses and Dissertations

A graph vertex coloring is an assignment of labels, which are referred to as colors, such that no two adjacent vertices receive the same color. The vertex coloring problem is NP-Complete [8], and so no polynomial time algorithm is believed to exist. The notion of a graph vector coloring was introduced as an efficiently computable relaxation to the graph vertex coloring problem [7]. In [6], the authors examined the highly symmetric class of 1-walk regular graphs, characterizing when such graphs admit unique vector colorings. We present this characterization, as well as several important consequences discussed in [5, 6]. By appealing …

Local Rings And Golod Homomorphisms, Thomas Schnibben

Theses and Dissertations

The Poincaré series of a local ring is the generating function of the Betti numbers for the residue field. The question of when this series represents a rational function is a classical problem in commutative algebra. Golod rings were introduced by Golod in 1962 and are one example of a class of rings that have rational Poincaré series. The idea was generalized to Golod homomorphisms by Levin in 1975.

In this paper we prove two homomorphisms are Golod. The first is a class of ideals such that the natural projection to the quotient ring is a Golod homomorphism. The second …

Geometry Of Derived Categories On Noncommutative Projective Schemes, Blake Alexander Farman

Theses and Dissertations

Noncommutative Projective Schemes were introduced by Michael Artin and J.J. Zhang in their 1994 paper of the same name as a generalization of projective schemes to the setting of not necessarily commutative algebras over a commutative ring. In this work, we study the derived category of quasi-coherent sheaves associated to a noncommutative projective scheme with a primary emphasis on the triangulated equivalences between two such categories.

We adapt Artin and Zhang’s noncommutative projective schemes for the language of differential graded categories and work in Ho (dgcatk), the homotopy category of differential graded categories, making extensive use of Bertrand Toën’s Derived …